{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from linear_model_for_classification import (\n",
    "LeastSquareClassifier,\n",
    "FisherLinearDiscriminant,\n",
    "LogisticRegression,\n",
    "SoftmaxRegression,\n",
    "BayesLogisticRegression\n",
    ")\n",
    "from linear_model_for_regression import Polynomial\n",
    "np.random.seed(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def create_data(size=50, add_outlier=False, add_class=False):\n",
    "    assert size % 2 == 0\n",
    "    x0 = np.random.normal(size=size).reshape(-1, 2) - 1\n",
    "    x1 = np.random.normal(size=size).reshape(-1, 2) + 1\n",
    "    if add_outlier:\n",
    "        x = np.random.normal(size=10).reshape(-1, 2) + np.array([5, 10])\n",
    "        return np.concatenate([x0, x1, x]), np.concatenate([np.zeros(size//2), np.ones(size//2 + 5)])\n",
    "    if add_class:\n",
    "        x = np.random.normal(size=size).reshape(-1, 2) + 3\n",
    "        return np.concatenate([x0, x1, x]), np.concatenate([np.zeros(size//2), np.ones(size//2), 2*np.ones(size//2)])\n",
    "    return np.concatenate([x0, x1]), np.concatenate([np.zeros(size//2), np.ones(size//2)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 1.3 Least Square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "x_train, y_train = create_data()\n",
    "feature = Polynomial(degree=1)\n",
    "model = LeastSquareClassifier()\n",
    "model.fit(feature(x_train), y_train, batch_size=5, epochs=60, lr=1e-3, use_SGD=True)\n",
    "model1 = LeastSquareClassifier()\n",
    "model1.fit(feature(x_train), y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EjSYxhMmUEuwBNaQiFpWIOEZhJFGhWXVN4O5Co7+Krk4xKUXEKQojiRoFUngs7yTqv150aJvTYlOMiEMURhJVCqQweI4C79khnrTAMwC8k2JakkisKYwk6hRIjbOypmBlXQ1Wu0Me9YL3HKy8WWClOVWaSEzopleJiQM3wm7evode3do6XU78sSzIPAPLezrYBWAC4O4EVrrTlYnERFR7RrNnz+b4448nNzeXDh06cN555/H55583/kJJSuohhcGywN0VPD0URJJSohpGixcv5vrrr2fZsmUsWLAAv9/PpEmTKC8vj+ZpJY4pkESkPpYxprEbHCJm9+7ddOjQgcWLF3PiiSc22r6kpIT8/HyWr/qCnNzcGFQosXJg7bqEGLIL7APf25iaVUAAPEcHZ7e5OztdmUjcKy0pZWiXIRQXF5OXlxeyXUyvGRUXFwPQpk2bep/3+Xz4fL7a70tKSmJSl8RewlxDql6PKf0dUE3tjan+rzBVL2Pl3AAZE52sTiRpxGw2nTGGGTNmMG7cOAYPHlxvm9mzZ5Ofn1/71b1791iVJw6I+yG7QNGRQQQE7wkymLK5wS0fRKTFYhZGN9xwA2vXruWpp54K2WbmzJkUFxfXfm3bti1W5YlD4jqQfG9zZBAdyoWp1AKmIpEQk2G6n/3sZ7z00ku89957dOvWLWS7jIwMMjIyYlGSxJF4HbILXiNq6JKqDdWfxKockaQW1Z6RMYYbbriBF154gYULF9K7d+9onk4SWHz2kMLZZVU7sYpEQlTD6Prrr+fJJ5/kX//6F7m5uezcuZOdO3dSWVkZzdNKgoq7QPIMouFfERekDYpVNYnNroCqtzDl/4CK5yGw0+mKJM5EdZju/vvvB2DChAl1Hp83bx5TpkyJ5qklQcXTluWWdxKm6sUGWthY3jNjVU7iqlqAKX8EqAHcGGyonA/p38fKuVZLHQkQ5TCK4S1MIpHn7oiVcyOm7K8EN787MCTnAmyszEsgfYhz9SUC34eY8vsPeSBw8I/VCzFFn2HlXBfshVoNbTAoyU5r04k0JONELHf34Ky5mk+Ca8alHY3lPQvSj3W6uvhmDKYi9OxZAOxvMSX/C2kjsXJnqJeUwhRGEpfiamadpzdW7s+criLx2AVgbw+vbc1HmIp/YmX/JLo1SdzSFhISd+JuIoM0j2niRKWqN8DWupWpSmEkcUmBlARcHQheawuXH2o2RKsaiXMKI4lbCqQE58qDtFE07WPGH61qJM4pjCSuKZAcZgzYJcGvZsyOtbKngJVH2D0kj26MT1WawCBxL16XC0pqxoBvAabyv2B/G3zM1Qkr8zzIODX8adju9lj5dwdn1VW/20BDF3iGBne3lZSknpEkBPWQYsgYTPmDmPIHDgYRgL0TU/5A8PGm9JLc7YKzEfP/ClYrjuwlWWC1Cd5vJClLYSQJQ4EUIzVrwfdW6Od9C6BmdZMPa3m6Y7W6F7wXgdUacIHVBrznQ+7/AKZZQ4GSHDRMJwlFQ3bRZ6re4MAqE/VzYarewEo/rukHd+VhZV8K2ZeCXYapfAqqXoGqF4Lro7t7YWX+ADJGNbt+SUzqGUnCUQ8pygKbaXg1chv8m1t2DrscUzwTqt4kuGfUwXObsruh8rWWHV8SjnpGkpAi0kPyb8JUvgb+DQRX4D4O3N2gein4P9//2FCszHNTa3VuK7PxNq4w2jTAVL4QXKEhxH5RpuIxrPQx4G7VovNI4lAYScJq0Qrfla9gKh6jznCU7/Uj29WsxNQsx8q+FrynNbfUhGKlj8FUbiH0xoIWVvrY5p/A2FD1VgPHJ/ic713IOr/555GEomE6ST01n+0PImh8c7zg86b8QQiEuc5aovNOArKp/+PBFXwuY1Lzj2/KgMaW/XFh7ILmn0MSjsJIUo6pfIWm/9V3YaoamGGWTFx5WPl37p+GDeDe/wVY+Vj5vwV3fvOPb2WE2S6r+eeQhKNhOkk9Netp+nbhNvg3RqOa+OTphdX6Aaj+GOP/FADLMwjSR4LVwo8NKwPSjoealYT+7xBo2VCgJByFkSS8pk9iaO4mbim2147lgYwxWBljIn/ozIswNStDPOsCz2Dw9Iv4eSV+aZhOElqzpnmnD6E5f/WttBFNfo2EkNYPK+c24MBQnJva/yaeYVi5t2rn1xSjnpEkvKZO87a8Z2Gq32/CGSwgE7wnN7tGqUfGCKz0x6D6Q4x/K5aVAekngKeX05WJA9QzkqTQpB5SWn+s7Gv2f3Por0Cof4lnYuX9JrglgkSWlQ4ZJ2FlXw5ZP1AQpTD1jCRpNKmH5D0dyzMQU/U61HwKuCB9OKSPwapZjanZCLix0odCxkRwaWaXSDQpjCSpNCmQPL2wcn565ONp/Zo9xUFEmkfDdJJ0tHadSOJRGElSSthAMgZMHG29HdgNvvfAtxgC3zldjSQxDdNJ0kqo7SYCOzGVLwY/9PGBlQ8Zk7AyzwFXdpTPXQDVK8HUBLf9ThsGpgxT9neo+bhuW89AIBfs7WB5sdJHB5cPSsbJHSYA1auCGwxaWZB+fHL+nHFCYSRJLSECyf81pvh2glsp7F+RwBRD1XOY6vex8mdH50PQrsSU/Q1qPiI4k9AKnt9qF7zh1a6nJ3TYKhSmcjNUvhRcIsjTO/I1OqV6Dabsr2CKCL4vBsrd4D0TK+sKsDSoFGl6RyXpxfWQnTGY0jmAjyOXxjFg78KUPx6l884+pOdjDp7fFIK9s5566j0QUIEp+X/BnlUyqPkcU3rX/iCCg6uLB6DqJUz5ow4VltwURpIS4jaQatbt/+APtZ2CDdVLwC6N8HnXg399A+dtCjv4wV29LALHcp6pmE+DQex7PXgtTSJKYSQpIy4DKfANja+VF4j49hWmegmR/fV3Y2rWR/B4DgkUhxHSFviasoKHhENhJCkl/gIpjbB6J1Z6ZE9rl9H0lcsbE4leltPC6YG6MCbCPVVRGEnqiatASv9e422sVuDuFdnzujsS2V//AFYybM1utaHx9yWA5W4fi2pSisJIUtKBQHKcuxOkjaahoTor83yw3BE9reU9mcj1jCyw8iAZ9h9yZUH6GBr+aPRA+vhYVZQyFEYiDrNybgDPsfu/c9X9X+854D0r8id1dwPv+SGedIGrC6SNp3aH1zqsw/7sxcr7NVjJsd+TlfUjgltb1P/xaGVdCa6cmNaUCnSfkYjTXJlYeXdAzafBiQV2Kbg7BHsv7u5RO62V9WNwtcNUPg9m7/5HPZAxASvrcnDlgj0Vaj4HwHj6YQW+wVS9Af5vwPJC+mgs72ngbhO1OmPO3Qmr1R8xZY+Af9XBx13tg0GVcZJztSUxhZFIPLAsSB+MlT44tufMPCMYJoGtwfuE3F3qrvjgyoOM44PNAdzHYaUfF7saneLujJX/vxAohMDO4PCdu7c2/IsihZGktLhemSFWLJf2EQrF3S74JVGna0aSsuJqVp1IilMYSUpTIInEB4WRpDwFkjTIrgTfB1D1FlSvC27zIRGna0YiJMjq3hJbxkDlc8HZhlQffNzVHiv7Bkg/NuRLpenUMxLZTz0kOZSpeBpT+RR1ggjALsSU3lk75V0iQ2EkcohkCaSdX+9i2csr+Pi1VRTtLnG6nMQTKIaq50M8Gdxuw1Q8GcuKkp6G6UQOk8hDdvt27uPx/32GTau+Ofigy+KE04/jktvOIyMrw7niEkn1BzS8XJIB/6cQ2APuxPo7Eq/UMxKpRyL2kMqKypkz9QG+Xrel7hO2Yfmbq7l/xhPYgUiv1J2cjF1M/UshHd5Qvc5IUc8oBQX8AdYu3sBHr35Cyd5S2nVty5hzj2fg8X0b31onhUSsh3Rg9lWU795/798fUlxYgqkncEzA5ssVX7Hhw88ZPO7oqNaRDCx3WwyBMBom0TJIDlMYpZjK0irm3vAwWzZsx3K5MLbNto07WPnWaoZNPJaf/P5S3J7IrhCdyFoUSNWrMZUvgn8dYMDdFyvzbEgfF5VgWvrS8nqD6ADL7eKjVz9RGIUjfSyUPwL4QzSwwGqFKZoebOPuhZU5GdInaMmgZtIwXYp5YtYzbN1YAICxgx9cB4Zu1ry7nlceWOBYbfGqWUN2lS8HZ1wdumto4CtM2V8w5Q9H5V6VsqLyBp83AZuSQm0KFxZXdnB17pBMcKt1fAR34v0aUzYXU/YX3YfUTAqjFFK4fQ/r3ttQG0KHMxgW/3sp1VU1Ma4s/jUpkPzbMBXz9n9z6Hu9/0PK9wZUr4hofQD57fIafN7lcdG6U6uInzdpZZ4ZvJ/Iah2igTnyz9Xvg+/taFeWlBRGKWTjx5sabeOr9LFlw7YYVJN4wgmkipJKtq+dR6DByw0uTNWrkS0OGHveCeAKPURk+21GnzMi4udNat7vY7V+GCvvd1g5vwLveY2+xFS+Ev26kpDCKIUY24Q1PyHg14yrUBoKpG/WbuF/z/kD1RUbcTd42c0G/1cRr+3Ei0fRsUc7LE89v9Yui6ETBjNgRJ+InzfpWS5IOxoyRoD9HY3O8rG3gQl1rUlC0QSGFNL72B40Nprt9rjpPrBLTOpJVAcmNRyqvLiC//v5o/gqqqmpBmMHP8NCisKuqN5sLzMens7Tf3yRVQvXMfj4csZNLqJz72o86TnkdvoemNLgFuHSTB6CYdTob1IMakkuCqMU0m1AF3oN7sGWz7bXO+vKcrk44YzvkZ2X5UB1ie3D/y6nqqIabMO6ZTn0PbaqgX8/uyB9ZFTqyGmdw7TZl+HbM4d060uMsbAsAxSB7xmM71Ws/P8Hnh5ROX+ys9KHY6rfa6CFCzxDNKOuGTRMl2J+8rsfkdc6B+uwXxYLi659O3HRjLMcqiyxrf9gI9jBfy0veyuPylIXgZAjNS6szDOjV0zVq6RbHwLsD6IDDFCOKbkLTBj30MiR0keB1ZbQH502VuZ5MSwoeSiMUkzbLq351VM3cda1k2jbpQ3eLC+d+3TiopvP4ZePXoc3x+t0iQnJX3Pww72yzM3cX3WlosyFMRAIgG0HvyANK/dWcHeLTiHGYCpfaqCBDaYQqj+JzvmTnZWGlT8LrFaHPwFYWNnTIX1I7OtKApYx8TspvqSkhPz8fJav+oKc3FynyxGp41v/jtobYV+491UWPvV+neHPNK/NiAmlDDyuArcbyiu6M+6S28AVxb/LgUJM0TWNNHKDdzJW9lXRqyPZGR/4PsBULwdTDZ7eWN5Twd3R6criTmlJKUO7DKG4uJi8vNDXK3XNSKSZOnu6snl7MJDGXTCSd/61pM7zNVUuPnwjnw/fyAfgp/defmQQmRqofh/jWwamCjy99n+oNbfnFO61Cl3TaBErIzjt2/t9pytJGhqmE2mBYCDtoUOPdvzoVxeCFby59ADLHfzzqZefxOCxA+q+OLALU3QDpmwu1CwPLhtU9Sqm6OdQ8Z/mFeRqA1a7RhoFsDzHNO/4IlGinpFICx3oIY0973g69+7Awn8tYcOHX2DbNr0H92TipWMZctKgui8yNqbkTrAPv18pOMxnKv+J5e4EGaObVoxlYWWei6l4NEQDF7jaQfrwgw/5t0HN/vXz0gaCR/ciSewpjEQi4EAgHTW0J0cN7dn4C6pXgv1tAw0sTOV/sJoaRgDeyeD/BqoXEhz8OGQav5WLlffr4E1QgWJM2Z/3L+R6CE9frJybwd2+6ecWaSYN04lEyIEhu3AY/yoavjHSQGAT2JVNL8SysHKux8r9DaSNAFcncPfGyroCq9XfwN0dTA2m9H+DG8Qdzv81pvjXYDe88KpIJKlnJHGpvKSC1Qs/pbyonDadWjFkwjGkeyO/akGkHTqpoUFh3+fTzGVlLAvSh2GlD6v/ed8SCGwP8eL90799b0Pmuc07v0gTKYwkvhh47ZG3eeOxdwn4/bjcLuyATUZWBj/4n3MYdXb8L/QZTiBZnr4YXyPbdVjtwMqJcHVBxrcojDYLsRRGEiMappO48sa8d3n1oQUE/MEewYG9lnwVPv5557N88va6hl4eNxodsksfB2Q2eAwr88zoLStjihtvY2tLbYmdmITRfffdR+/evfF6vQwfPpwlS5Y0/iJJOVXlVbzx2DsNtnlx7msYO/L3adf4agj4Dxk6M0D1ekzp3zAlv8GU/gWqVzVp47QGA8mViZV7C8HBiXp+DdOOB28Ul2Zydar/vIfSDZwSQ1EfpnvmmWe46aabuO+++xg7diwPPvggZ5xxBhs2bKBHDy3WKAetX7KRGl/DG/vtKdjL1o076Dmo5cvp2LbNB//5mIVPvc93W3YD0G94H067chwDj3kZaj7i4Gw0F6Z6CaQNwcqdGbzpMQwNDtmlD8Vq9afg/je+pYAP3N2xvJMhYwJY0Vv52co4FVOzvJE2k6J2fpHDRT2M/vznPzN16lSmTZsGwL333subb77J/fffz+zZs+u09fl8+Hy+2u9LSjRMkErKSiqwsDCNLM9fUdKMGWaHMbZh3u1P8cmCtXUe37TqGwZ/7yMG9CvaP0J2YFr0/v+tWYcpewgr92ctrgEIhk/OTyHnp5E5XrjShwd7X/UGkgWegZAxPjLnChRB9QcYuwTL3Q7Sx4JLK8NLXVEdpquurmblypVMmlT3X1iTJk1i6dKlR7SfPXs2+fn5tV/du3ePZnkSZ9p1adNoEEFwsdeW+vj1VUcEEUBGhp/xZxUdttr1oQxULwa7qMU1OMqysHL/B7znA4cujpsO3jOw8n7T8j2XjMGUz8cUTQvehFv1Aqb8fsy+q6DytZYdW5JOVHtGhYWFBAIBOnasO/bcsWNHdu7ceUT7mTNnMmPGjNrvS0pKFEgpZNDo/uS2zaVsT2m9kWS5XPQ+tgcdejS23E3jFj3zAZZlcfg6wUcdU0l6RmOBaAdXLIhUz8EpVhpW9uWQ9YPgTbIYcPcCV8MTK8JW+SxUPX/IAweuydVgKh7BcmVCxsTInEsSXkymdh++d44x5ojHADIyMsjICG8sXhKXsQ2fLfuCDcu+xPYH6Dm4O8NPGYIn3cNZ15zCU7OPXJfNcrnwpHv44S2RmWpcsGnnEUEE4PaEO0Ghaff/bN6+p/F7j5rDmJbPuLMygssARZJdial8vsEmpvxfWOknNbIlrqSKqIZRu3btcLvdR/SCvvvuuyN6S5Ia9n5bxN9//ig7N3+Hy+0GCxY/u5Tn5rxMvxFHsebd9fX2WPoPP4oLbjqLbv07R6QOT7oHf82RgbJtkxfbBldjn4+efmGf68A25RELJLs8uKBq1Ztg9gFZ+1eQPjt+lvCpWQE0PBkFswf8X0Q+CCUhRfWfJOnp6QwfPpwFC+re3LdgwQLGjBkTzVNLHPJX+/nrTx/iu22FANiBAPb+6dQVpRWseXc9QL09ln7fOypiQQQwbOJgXO4j//oXFXpY92E2gZALJLjAc0yTt3jo7OkKEPZyQSHZJZjiWzCVz+wPIoAKqHoNUzQD/FtbdvxIMRWRbSdJL+r94xkzZvDII4/w2GOP8dlnn/GLX/yCrVu3Mn369GifWuLMygVrKdyxp/ZG1qZY8I/F+CqrI1bL9380nuBm60d65u+dKNqdgTniWQusVli5P2/WOSMRSKb8UbB3wRFX1WygElP6pybdCxU1rk7htXOH2U6SXtTD6Ic//CH33nsvd955J8OGDeO9997jtddeo2fPMFY2lqSy6p219V4rDIev0seXK7+OWC1d+3Xi2nuuwONNw8LCcrlqe0qe9LaY3D/gyvwRWB2ANLDaQubFWK3+DK7mD4W1KJDsEqj+gDqrcNdtAPY28G9sdn0RkzakkX2V9k8fd3cB44+PABVHxWQCw3XXXcd1110Xi1NJHKsq99U7BBeu6gj2jAAGjx/I7NduZ9krK9jy2XbcHjfHjB7A0InH4Pa4gZ5YWRdG9JzQgmtI/q2EDqJD230NaUc3u76I2L9yuCm9i2DNh/53dwHp4O6L2XtNcFFWPJA+GivzPPD0dqJicZgWSpWY6dKnE1+t2dysYTqAzn0iP+klM9fLxEvHRfy4jWlWIFlh/rq29P6gSEkfipX3/zAVT4J/w8HHPUOD17t8rxzS2B+8Mbb6Q6zcX0Go1cYlaWlOpcTMuAtHNiuIgvcX9aTzUck1A7PJQ3aePkAYq3inHdf8oiItbSBW/l1YrR7Gyv8TVqt54DkKAlvqaWwDfkzpHDCR7QVL/FMYScx06dOJM68+FTjy3jMLcLldWK66j7vcLrxZGfz49sgPl8WDJgWSlRYcxgrdILjUTrxM7z6Uu21w+M2VDVVvcuQEjENV7L82JqlEYSQxNfmaU7jqrkvrDLnlt8vjnBvO4NdP/YITzvje/us14PZ4GDn5e9z25M/plGS9okM1KZAyz4faBUxddf/XcwxWdpxfm7X3AWWNNHJj/JvrPhTYBlXvgO9dCOyOUnHiJMu05IpylJWUlJCfn8/yVV+Qk5vrdDkSSQbKissJ+G3y2uTU6RH5q/1UlFaSlZuJJz11Lmt+698BEN41JP83GN/bwQ9mV15wJYO0wdHb/yhSAvswRVMbaeQC77nBpYoCezBlfwX/+rpN0kZj5VyvBVcTQGlJKUO7DKG4uJi8vLyQ7VLnN13iiwU5rbLrfcqT7iGvbXL/46OytIr172+ksqyKDj3a0v/4Pk2b1ODpjeW5OjbFRpK7dXD9u8DmBhrZWOnHg12OKfk12IVHNqn5CFNaiJX3u/Andkhc039FkRgytuHVh99mwT8W4a/2YxG8etK6Yyt+/JuLGXhC38guHRSHrMyLMWX3hHjWBZ6+4BkAlS+C/V2Idjb4v4TqjyFDq7kkA10zEomh//7fG7z+yNv4q4Pr4h0YIy/6rpi///wxvl67JXJLB8WrjNFYWVP2f3NgWHH/R5G7Z3Bqt2VhfA3v+gsWpmphdGqUmFPPSOLeji93suHDzwnUBOhxdFeOHtX/iFl3iaC4sJS3579X73PGGLBtXrrvTW564JrIL64abzLPwUofhal6BwLbweXFSh8TnJZ+YBVvu7HNNc0h6/NJolMYSdwqL6ngsV/9i40ffYnlcmFZYAds2nRuzTV3X073gV2dLrFJPlmwpsFlb4wxfLnyK4p2l9CqfV5tICUtdwes7EsbeL4tBBqaeecCV/LOskw1GqaTuGTbNv93/aN8vvwrAIxt194wu29XMfdOf4jCgr1OlthkZfvK610p/HDlRVrJGsDKOLWRFjaW9+SY1CLRp55RivBX+/FVVpOZ4w3rA7ElSveW8eHLK9i1ZTcZ3nS+d8oQ+h7Xm3qXyA5h/fsb2bpxe73PGdvGV1nNu/Pf5+Kbz4lQ1dHXulMrbH/DK1BYWOS3T+6ZhGHzngy+tyEQYk0+z3GQ9r2YlyXRoTBKcgVf7eT1RxeyeuE67IBNRlYGY849gdOmTCC3TRhLyzTR+y98xDN3/xdj2/uv61gsfnYpfYb1YvqfppCVF96W1ivfWoPlcmHs+j+8jW3z0eufJFQYDT91KM/OeaneTf0guOzRseOPDjnlPeVYGcG17cofhur3ORhIaeA9DSvr8vi/r0rCpmG6JPbVms3cfcVcVu0PIgBfhY9Fz3zAH6+cS3FhaUTPt37JRp6a/QJ2IIAxBjtgY+/fpe7rtVt56NZ/hn2s8uKKkEF0gK/C16J6Yy0z18v5N55Z73OWy0W6N41zbzjjiOeSdlZdOFzZWLk3YbV6FCv311i5v8FqPQ8r+yfxsyCsRITCKEnZts2825/CXxPAHLY4qbFtinaX8NyfX47oOV975O2Q+xUZ2+bLFV+xZUP9Q2+Ha9+9baPDiW07t2lyjU6b8MMxXH7HD2jVoVWdx/sO68XN866nU6+668ol/TTvcLnzIX14cDVvrbqQlDRMl6Q2LvuSfTuLQj5vAjarFq6jbF8ZOa1bPlxXureMLRu2NdjG5XaxZtF6eg5qfMvuseeN5L1nPwz5vIXFuAtH1X5fuGMvi/+9lM8+/IKAbdP/e0dx4sVj6Nov/nYSHXXWcE6YfBxbPt1OZVkV7bu1oX330BvRJf00bxEURkmr4KtdDV5zgWAg7dpaGJEwqq6qabSNZVlUV9V/veRw3fp35vuXjmfhU0uOPI7LRbf+XTjxomAYrX1vA4/c+iS2bWp/3sLte3j/Px9x6cwLGHfByCb8JLHhcrnofWyPsNsrkCTZaZguSaV708FufA3cDG96RM6X3z4Xb7a3wTYBf4AuTdgg78JfnMXFN59Lq/b5tY+ledM56aLR3PTgNaR709j7bRGP3DqfgD9QJ3gPXCN7avYLbP604R5botCQnSQz9YyS1LHjB/Lvuxtu06pDK7pEaBjLk+Zh/AUjeXv+knp7YxaQnpnB8ElDwz+oBRN+MIYTLxrFzm++I1AToEOPdmRkZdQ2WfLCMuwGen8ut4tFz3zAlDsvacqPE7fUQ5JkpZ5RkmrdqRUjzxoeckIBwBlTv4/LFbm/AqdP/T5d+3TEOuyYlssFLhdT/t8lZGQ2vSfmcrno0qcT3Qd2rRNEAJ8v39TgUKQdsNn40ZdNPmc8Uw9JkpHCKIldOvN8hk44BgCX271/J1UXFhZnXnMq486P7LUUb7aXXzzyU06/aiLZ+++VsSyLwWMH8MtHfsqQkwZF9HxAg8vrHGwT+dM6TYEkyUbDdEnMk+7h6rsvZ9vGHSx/YzXlJRW07dya0WePoHWnVlE5pzcrg7OmT+LMa06lsqyKdG9aVDfI6z+8L1s3FoTsHbncLvof3ydq53eShuwkmSiMUkD3gV1jvqio5bLCXm2hObZs2M6Xn3yD5W74Dnw7YDPxh2OjVofTFEiSLBRGklD27Srikdvms3n9Vqz9Ww0YE+wVWS4Ls38Gocvtwg7YXHzzufQe0tOxemNBgSTJQGEkCaOqwsdfrnmQfbuKgIMhBMFJEhnedLJbZYGB/iOO4sSLR9Pj6MZvsE0GSb/dhCQ9hZEkjGWvrGRPiG0jjG3jq/Bx9k8nMeGS5B2WE0lWmk0nCePjV1c2+LzBsOzVT2JUjYhEksJIEkZZGJvOlReVx6ASEYk0DdNJwujQvS17dxaFnMZtuVy07+7MBXw7YLN28YbgxAqXi4Ej+zJgRN8mbSgYCZrEIIlKYSQJY9wFo/isgdUUjG0z7oJRIZ+Plq2fbefBX/6Dot3FuDxuMPDWE+/SpW8nfvrnq2jTuVVM6tCsOklkGqaThDFkwiCOGTuw3iWOLMti0OgBDPv+MTGtad+uIv523cMU7wluVGj7A7UbCu785jvunf5gWCuaR4pWZpBEpTCShOFyubjmnss59coJdVYI92Z7OfWKCVz7pysiutZeOBY/s5Sqiup6hw7tgM2egr2seHN1TGtSIEki0jCdJBRPmodzrz+dydNOpuCrXQB06dORtAxntqBe8eaaBhdqtbBYuWANY849PoZVachOEo96RpKQ0jLS6DmoGz0HdXMsiACqKqoafN5gqCxruM3hbNumrKicGl/LhvfUQ5JEop6RSAt07NWBLZ9uw4RYPdzldtHlqPA2FKwoqeStxxfx/n+WUVlWFVzxfPzRnDH15LC2aq+PekiSKNQzEmmBEy8aHTKIIHjdaGwYW3WUl1Rwz0/+ztvz36vtSRljWP/+Rub85D4+Xfp5s2tUD0kSgcJIpAWOP30Yx4yrf4YfwMRLx9P72B6NHufl+95i97Y9R1x/MraNCdg8fvvT+Kv9za5TgSTxTmEk0gIut4tr77mCs66dRG7rnNrH23Vty6UzL+CiX5zV6DF8ldUse3l5yIkQBkNFaQWr313foloVSBLPdM1IpIXcHjenT/0+k6ZMYO/OItxuF607tgp79YV93+6jppFej9vjpuCrnS2uVdeQJF6pZyQSIS63i3Zd2wR30W3CMkBp3vRG29i2IT2MduFQD0nikcJIxGFtO7emc59OWA0kmLFthk6I3OoSCiSJNwojkQirrqph2Ssref7Pr/DSfW+w+dNtEHrCHVhw5tWnYEI0slwujh0/iM5hThEPlwJJ4ollGpqX6rCSkhLy8/NZvuoLcnJznS5HpFGfLv2ceb/+F5VlVfsXTTXYAZt+xx3F1XMuJzsvK+RrFz39Ac/95RUwBmv/skZ2IMDRI/sx7e7L8WZlRKZIey9UrwFqwNOXbwkeV9eQJBpKS0oZ2mUIxcXF5OXlhWynMBKJkK2fbeeeq+7DBOwjejmWy0WvY7rzP49e1+D1pJI9pSx7ZSXfbSkkM8fL8ElD6XVM98hsRWF8mLIHoXoxdbpq7r7szPwRvXoOjMBJROoKN4w0m04kQt56fBFm//8dztg236zbwucrNjHg+L4hj5HXNpdJV06IfHEGTOkfoWYNR4wZBr6Gsv+DwJ3gbhP5c4uEQdeMRCIg4A+wetGnmEDoRVNdbjer3l4Xw6oOUbMOalZT/8UrG6jEVL0c25pEDqEwEokAf7W/wdW7Ibi8T1WFL0YVHXbu6kU0/OtuoOqdGFUjciQN00nS81f7WfXOela8tZqKkko69mrPuPNH0mtw94idIyMzg9w2OZTuLWuwXcee7SN2ziaxiwn2gOrXiSq27PTSq42BEEsbiUSTwkiSWnFhKX/76UPs3PwdlmVhjGHzp1v58KXlnHjxaH5483mRmRxgBRdNfe3ht0MvnGoMo88ZEYGTNYOrPcGeUQOBZGWyecdezaoTRyiMJO6U7i3jgxeX8/XazbhcLgaO7MeoM7+HN8fb+IsPZeDhm//Jd9sKg9/uDwl7/3Wd9579kI49OzDhh2MiUvfJl41n7eINbP/y2zpDdgdC8KIZZ9OqQ35EztVUVsb3Mb43G2qB5Z1EZ09XNm/foUCSmNM1I4kra9/bwO1nzeaVB97k0w82sn7JBp6b8xK3nz2bb9ZuadKxNn+6jW/Wb6kNn/q8/c/F2I1c6wlXRlYGNz10LadcNr7Otujd+nfh6j9ezoRLxkbkPM3i6QfpE6m/G+gCV0fwngmwP5B0I6zElnpGEjd2fvMdD9/yJHYgUPuY2f//q8p9/N/PH+O3/7mZnENWx27IZ8u+wHK7Gpzhtm9XEbu37YnYtRxvVgbn/XwyZ02fRFFhCWnpaeS3i4N75Cywcq7HVLaHqpfBVB58Im0kVs414Dr4vqqHJLGmMJK4sejpDwi1bo4xBl+Fj6UvrQj7PpxAwMbCanAlHqDBnlNzedI9tOsSZ/fsWC6srEsg83yo+QLwg6cnuOqvU4EksaRhOokba9/b0GAwGGNY+95nYR+v1+DudXpZ9cnM8dI+1T5srQxIPxbSjwsZRAdoyE5iRWEkcSPgbzg4gCbtdjpodH/adG5du87b4SzLYtwFo/Cka4CgIQokiQWFkcSNnoO7hwwOCO4XdFQ9W3jv21XExo++5Ou1W+oEmsvl4to5V+DNSq9z3ANbNfQ9rjdnXXtqBH+C5KVAkmjTPwklbkz4wVg+fX9jyOftgM2JF42q/X5PwT6euftFPv3g4GtyW+dw+rSTmXDxGLCCM9luf2YGi55eykevf0JVuY8O3dsy/sJRjDp7OJ40/QqES9eQJJq0arfEDwMvzn2NBf9cjOVy1d6rc2BG3MU3n8uEHwTvCSr6rpg/XP43yooq6l2G54xpp6jXEyXf+hVIEr5wV+3WMJ3EDwvO+9lkrrnnCvoO64Xb48aT7mHw6AHceP81tUEE8PojCykrrj+IAN545B327SqKUeGpRUN2Eg0ao5D4YsHQCcc0uMW2v9rPR6+uaPD+IVwWH73yCadP/X4UihQN2UmkqWckCaeitJKaRmbVWS6LvTv3xaii1KQekkSSwkgSTmaOt8FZdwAYQ07r7NgUlMIUSBIpCiNJOGkZaRx38uAGA8kO2Jxw+nExrEpEWiJqYbR582amTp1K7969yczMpE+fPtxxxx1UV1dH65SSQiZPOwVPmhvLdeTCnxYWI88cTqejOjpQmYg0R9QmMGzcuBHbtnnwwQfp27cv69ev5+qrr6a8vJw5c+ZE67SSIjof1ZGbHriWx//3KXZv34NFcFU7l9vN+AtHcuEvzgr7WMWFpbz/wkd8smAtviof3fp34cQLRzFo9IDI7HUkIo2K6X1G99xzD/fffz9ff/11vc/7fD58voPbMpeUlNC9e3fdZyRgoLy0ArfHjTcro87jX37yNQVf7SIjM41jxg4kt014q3oDbP1sO3+77mGqKqprp4m73C7sgM24C0Zx6W3nK5Aa8a1/B4Bm1km9wr3PKKZTu4uLi2nTJvTCjLNnz+a3v/1tDCuSeBfwB1j0zFLeffp99u0sAqD3sT2ZNGUCQ04cBBb0G34U/YYf1eRj+6v93HfjvDpBBAdX8X7/hWX0OLobY887PiI/S7Lq7OnKt/4dbN6+R4EkzRazCQxfffUVc+fOZfr06SHbzJw5k+Li4tqvbdu2xao8iUN2wOahm//Jf+59tTaIADav38qDv3yCd+YvadHxV72zntJ9ZSFvnLWAd55cHGpXCzlEZ09XAM2sk2ZrchjNmjULy7Ia/FqxYkWd1xQUFHD66adz8cUXM23atJDHzsjIIC8vr86XpK4PX1rB+vc/wxyWBgdGll+49xV2799SvDk2rfoGl9sd8nkD7Nqym/LSimafI5UokKQlmjxMd8MNN3DJJZc02KZXr161fy4oKGDixImMHj2ahx56qMkFSupa9O8P9m+OV3/XxHK5+OA/yznv52c06/iWRVjXgyxdNAqbhuykuZocRu3ataNdu3Zhtd2xYwcTJ05k+PDhzJs3D1djNypKXNmyYTuL/72UTZ98g8vt4pgxAzjph2Po0CO8//4ttfOb70IGEYCxbXZ8tbPZx+87/CiWvLAs5PMWFp16dyArN7PZ50hFCiRpjqhNYCgoKGDChAn06NGDOXPmsHv37trnOnXqFK3TSoS8+9T7PPfnl2tnlgEsfn4v7z2/jGl/uKzBteMiJS09DV+lL+TzlmWRkZnW7OMPm3gMee3yKN1b/3Ujg+GUy0/UbLpmUCBJU0Wtq/LWW2+xadMmFi5cSLdu3ejcuXPtl8S3r9Zs5rk/vwxQZxtwE7CxAwEenTm/zoSCaDnu5GNxuUP/FTXGMPSkwc0+vifNw/V//UlweSHrYOIcOOeEH45l1Fkjmn38VKdrSNIUUQujKVOmYIyp90vi27tPvd9gCNi2aXB4K1JOvmx8cFJMPV0Ty+2ibZc2HHdy88MIoFv/ztzx3C8557rT6T6gK+27t2PYxMHc9MC1XPzLc9QraiEFkoRLW0jIEb5Y8XWdHtHhjG3zxfL6b1yOpC59OzH9T1fyyG3z8VX6ame+2YEA7bu24Ya50/Ckt/yvcE7rHCZNmcCkKRNafCw5kobsJBwKIzmCFU5vIEY9hkFjBvD7N37NijdWs/nTbXjSPAweO5BBY/trQkwCUSBJYxRGcoT+x/dl9cJ1IXtHlsvFwBP6xqweb1YG4y4YybgLRsbsnBJ5BwJJpD76p6Uc4fuXjgsdRIDb7UrKYPBX+6koqcTYuq4pEmvqGckReh/bg0tuPZ+n//ifOlO7LZcLl8vF1X+8nFYd8h2uMnK+WbeVN+ctZP37GzHGkNMqm/EXjuKUK06quyiriESNwkjqNf6iUfQe0pMlz33IFyu/xu12MWjMAE68eDTtuoZe7DbRrF28gYdu+SdwcJmhsqJy3pj3Luve28AvHvmpAkkkBhRGElK3/p259FcXOF1G1Pgqq3n8N0+DbR+xzkNwdYddvPHIO5z388mO1JesNIlB6qNrRpKyVr61Bl+FL+SCQ8a2WfLCR/hr/DGtK5npviMJRWEkKatg007cntCrdgNUlVdRUlgWo4pSgwJJ6qMwkpSV5k0jnAVB0jI0mh1pCiQ5nMJIUtbQCcdgBwIhn7csi56DujdpG3MJnwJJDqUwkpTVa1B3+g0/CivESg7GGM6YenKMq0otCiQ5QGEkqcuCa+6+gqOG9ADA5XbjcruwLAuX28Ult53PsSce7XCRyU+BJKCp3ZLisvIymfHQT9m06htWvbOOqkofHXu2Z/TZIxwbntu8fhvv/GsJGz/6Egz0G34UEy8dS7/vHeVIPbGgtevEMnG8p0NJSQn5+fksX/UFObm5TpcjEnXvv/ART81+oc7KFwf+fPwZxzF43NH0GtSNdkn6gX1g7ToFUvIoLSllaJchFBcXk5eXF7KdekYicaLgq508NfsFoO6mhgf+vPz1VSx/fRUAR4/qz49/czGt2of+5U5E6iGlLl0zEokT7z27rMFNDQ+1cfkm/jT1PipKKqNcVezpGlJqUhiJxIlNq79pcFPDQ5mAzb6dRbz33IdRrsoZCqTUozASiRPuJm4WaIxh6YvLo1SN8xRIqUVhJBInBo0dEPKep1BK9pZGqZr4oEBKHQojkThx4oWjcHtcWE3Y0z2vbfLPMlUgpQaFkUicaN2pFdfOuRJPuhvLajyQLMti7HnJt+NufQ4EkiQvhZFIHBk0uj+//e9tTJ52CkcN7UVmjrfedpbLRdsubTjxolExrlAkOnSfkUicyW+Xy+RrTmHyNafgr/bz3F9eYemLywn4D+6rNGhMf358+0Vk5tYfViKJRmEkEsc86R4uufU8zv7pJDZ9Epz63ePobrTt0trp0kQiSmEkkgCy87IYOuEYp8twnFZmSF66ZiQiCUGz6pKbwkhEEoYCKXkpjEQkoSiQkpPCSEQSjgIp+SiMRCQhKZCSi8JIRBKWAil5KIxEJKEpkJKDwkhEEp4CKfEpjEQkKSiQEpvCSESShgIpcSmMRCSpaLuJxKQwEhERxymMRETEcQojERFxnMJIRJJOZ09XTWJIMAojEUlKCqTEojASkaSlQEocCiMRSWoKpMSgMBKRpKdAin8KIxFJCQqk+KYwEpGUoUCKXwojEUkpCqT4pDASkZSjQIo/CiMRSUkKpPiiMBKRlKVAih8KIxFJaQqk+KAwEpGUp0BynsJIRAQFktMURiIi+ymQnKMwEhERxymMRETEcQojERFxnMJIROQwum4UewojEZFDdPZ0BRRIsaYwEhE5jAIp9hRGIiL1UCDFVkzCyOfzMWzYMCzLYvXq1bE4pYhIiymQYicmYXTLLbfQpUuXWJxKRCSiFEixEfUwev3113nrrbeYM2dOtE8lIhIVCqTo80Tz4Lt27eLqq6/mxRdfJCsrq9H2Pp8Pn89X+31JSUk0yxMRCVtnT1e+9e9g8/Y99OrW1ulykk7UekbGGKZMmcL06dMZMWJEWK+ZPXs2+fn5tV/du3ePVnkiIk2mHlL0NDmMZs2ahWVZDX6tWLGCuXPnUlJSwsyZM8M+9syZMykuLq792rZtW1PLExGJKgVSdFjGGNOUFxQWFlJYWNhgm169enHJJZfw8ssvY1lW7eOBQAC3281ll13GE0880ei5SkpKyM/PZ/mqL8jJzW1KmSIiUfWtfweAhuwaUVpSytAuQyguLiYvLy9kuyaHUbi2bt1a55pPQUEBp512Gs899xwjR46kW7dujR5DYSQi8UyB1LhwwyhqExh69OhR5/ucnBwA+vTpE1YQiYjEuwOTGqTltAKDiIg4LqpTuw/Vq1cvojQiKCIiCU49IxERcZzCSESkhTTNu+UURiIiLaD7jiJDYSQi0kIKpJZTGImIRIACqWUURiIiEaJAaj6FkYhIBCmQmkdhJCISYQqkplMYiYhEgQKpaRRGIiJRokAKn8JIRCSKFEjhURiJiESZAqlxCiMRkRhQIDVMYSQiEiMKpNAURiIiMaRAqp/CSEQkxg4EkhykMBIREccpjERExHEKIxERcZzCSETEIZrEcJDCSETEAZpVV5fCSETEIQqkgxRGIiIOUiAFKYxERBymQFIYiYjEhVQPJIWRiEicSOVAUhiJiMSRVA0khZGISJxJxUBSGImIxKFUCySP0wU0xBgDQFlZmcOViIjEXi557AwU8OnGMnp0aeN0Oc1SVhr8/D7weR5KXIdRaWkpABPHf8/hSkREpCVKS0vJz88P+bxlGosrB9m2TUFBAbm5uViW5XQ5AJSUlNC9e3e2bdtGXl6e0+XELb1P4dH7FB69T+GJx/fJGENpaSldunTB5Qp9ZSiue0Yul4tu3bo5XUa98vLy4uY/djzT+xQevU/h0fsUnnh7nxrqER2gCQwiIuI4hZGIiDhOYdREGRkZ3HHHHWRkZDhdSlzT+xQevU/h0fsUnkR+n+J6AoOIiKQG9YxERMRxCiMREXGcwkhERBynMBIREccpjERExHEKowjw+XwMGzYMy7JYvXq10+XElc2bNzN16lR69+5NZmYmffr04Y477qC6utrp0hx333330bt3b7xeL8OHD2fJkiVOlxR3Zs+ezfHHH09ubi4dOnTgvPPO4/PPP3e6rLg2e/ZsLMvipptucrqUJlEYRcAtt9xCly5dnC4jLm3cuBHbtnnwwQf59NNP+ctf/sIDDzzAr371K6dLc9QzzzzDTTfdxK9//WtWrVrF+PHjOeOMM9i6davTpcWVxYsXc/3117Ns2TIWLFiA3+9n0qRJlJeXO11aXFq+fDkPPfQQQ4YMcbqUpjPSIq+99poZOHCg+fTTTw1gVq1a5XRJce/uu+82vXv3droMR51wwglm+vTpdR4bOHCgue222xyqKDF89913BjCLFy92upS4U1paavr162cWLFhgTjrpJHPjjTc6XVKTqGfUArt27eLqq6/mn//8J1lZWU6XkzCKi4tp0yYx92aJhOrqalauXMmkSZPqPD5p0iSWLl3qUFWJobi4GCCl//6Ecv3113PmmWdyyimnOF1Ks8T1qt3xzBjDlClTmD59OiNGjGDz5s1Ol5QQvvrqK+bOncuf/vQnp0txTGFhIYFAgI4dO9Z5vGPHjuzcudOhquKfMYYZM2Ywbtw4Bg8e7HQ5ceXpp59m5cqVrFixwulSmk09o8PMmjULy7Ia/FqxYgVz586lpKSEmTNnOl2yI8J9nw5VUFDA6aefzsUXX8y0adMcqjx+HL5HlzEmbvbtikc33HADa9eu5amnnnK6lLiybds2brzxRubPn4/X63W6nGbT2nSHKSwspLCwsME2vXr14pJLLuHll1+u8+ERCARwu91cdtllPPHEE9Eu1VHhvk8HfjkKCgqYOHEiI0eO5PHHH29wk61kV11dTVZWFs8++yznn39+7eM33ngjq1evZvHixQ5WF59+9rOf8eKLL/Lee+/Ru3dvp8uJKy+++CLnn38+bre79rFAIIBlWbhcLnw+X53n4pXCqJm2bt1KSUlJ7fcFBQWcdtppPPfcc4wcOTJuNwV0wo4dO5g4cSLDhw/nySefTIhfjGgbOXIkw4cP57777qt9bNCgQZx77rnMnj3bwcriizGGn/3sZ/znP/9h0aJF9OvXz+mS4k5paSlbtmyp89hVV13FwIEDufXWWxNmSFPXjJqpR48edb7PyckBoE+fPgqiQxQUFDBhwgR69OjBnDlz2L17d+1znTp1crAyZ82YMYPLL7+cESNGMHr0aB566CG2bt3K9OnTnS4trlx//fX861//4r///S+5ubm119Ty8/PJzMx0uLr4kJube0TgZGdn07Zt24QJIlAYSZS99dZbbNq0iU2bNh0R0qncKf/hD3/Inj17uPPOO/n2228ZPHgwr732Gj179nS6tLhy//33AzBhwoQ6j8+bN48pU6bEviCJGg3TiYiI41L3KrKIiMQNhZGIiDhOYSQiIo5TGImIiOMURiIi4jiFkYiIOE5hJCIijlMYiYiI4xRGIiLiOIWRiIg4TmEkIiKO+//ugKW60S1owQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train)\n",
    "x1_test, x2_test = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.concatenate([x1_test, x2_test]).reshape(2, -1).T\n",
    "y_pred = model.classify(feature(x_test))\n",
    "plt.contourf(x1_test, x2_test, y_pred.reshape(100, -1), alpha=0.2, levels=np.linspace(0,1,3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.title('least square')\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 1.4 Fisher discriminant function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = FisherLinearDiscriminant()\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train)\n",
    "x1_test, x2_test = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.concatenate([x1_test, x2_test]).reshape(2, -1).T\n",
    "y_pred = model.classify(x_test)\n",
    "x = np.linspace(-5, 5, 20)\n",
    "plt.contourf(x1_test, x2_test, y_pred.reshape(100, -1), alpha=0.2, levels=np.linspace(0,1,3))\n",
    "plt.plot(x, x * model.w[1]/model.w[0], label='w', linestyle='--')\n",
    "plt.title('Fisher Discriminant')\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(x, x * model.w[1]/model.w[0], label='w', linestyle='--')\n",
    "w = model.w\n",
    "rollmat = np.zeros((2,2))\n",
    "div = np.sqrt(w[0] ** 2 + w[1] ** 2)\n",
    "rollmat[0,0] = w[0]/div\n",
    "rollmat[0,1] = w[1]/div\n",
    "rollmat[1,0] = -w[1]/div\n",
    "rollmat[1,1] = w[0]/div\n",
    "x_proj = x_train@w\n",
    "x_proj = np.concatenate([x_proj[:,None], np.zeros_like(x_proj[:,None])],axis=-1).reshape(-1, 2)\n",
    "#plt.scatter(x_proj[:,0], x_proj[:,1]-5, c=y_train)\n",
    "x_roll = x_proj @ rollmat\n",
    "plt.contourf(x1_test, x2_test, y_pred.reshape(100, -1), alpha=0.2, levels=np.linspace(0,1,3))\n",
    "plt.scatter(x_roll[:, 0], x_roll[:,1], c=y_train)\n",
    "plt.scatter(0, 0, marker='x', alpha=1)\n",
    "plt.title('Projection')\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 2.1 Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_lr = LogisticRegression()\n",
    "model_lr.fit(feature(x_train), y_train)\n",
    "y_pred = model_lr.classify(feature(x_test))\n",
    "y_prob = model_lr.prob(feature(x_test))\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train)\n",
    "plt.contourf(x1_test, x2_test, y_pred.reshape(100, -1), alpha=0.2, levels=np.linspace(0,1,3))\n",
    "plt.title('Logistic Regression')\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.show()\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train)\n",
    "plt.contourf(x1_test, x2_test, y_prob.reshape(100, -1), alpha=0.2, levels=np.linspace(0,1,5))\n",
    "plt.colorbar()\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 2.2 Softmax Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "multi_x_train, multi_y_train = create_data(add_class=True)\n",
    "plt.scatter(multi_x_train[:, 0], multi_x_train[:, 1], c=multi_y_train)\n",
    "model_sr = SoftmaxRegression()\n",
    "model_sr.fit(feature(multi_x_train), multi_y_train, max_iter=1000)\n",
    "y_prob = model_sr.prob(feature(x_test))\n",
    "y_pred = model_sr.classify(feature(x_test))\n",
    "plt.contourf(x1_test, x2_test, y_pred.reshape(100, -1), alpha=0.2, levels=np.array([0., 0.5, 1.5, 2.]))\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### 2.3 Bayes Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train)\n",
    "model = BayesLogisticRegression()\n",
    "model.fit(feature(x_train), y_train)\n",
    "y_prob = model.prob(feature(x_test))\n",
    "plt.contourf(x1_test, x2_test, y_prob.reshape(100, -1), alpha=0.2, levels=np.linspace(0,1,5))\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.title(\"Bayes Logistic Regression\")\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from linear_model_for_classification.fisher_linear_discriminant import MultiFisherLinearDiscriminant\n",
    "# np.random.seed(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_data(size=50, add_outlier=False, add_class=False):\n",
    "    assert size % 2 == 0\n",
    "    x0 = np.random.normal(size=size).reshape(-1, 2) - 1\n",
    "    x1 = np.random.normal(size=size).reshape(-1, 2) + 1\n",
    "    if add_outlier:\n",
    "        x = np.random.normal(size=10).reshape(-1, 2) + np.array([5, 10])\n",
    "        return np.concatenate([x0, x1, x]), np.concatenate([np.zeros(size//2), np.ones(size//2 + 5)])\n",
    "    if add_class:\n",
    "        x = np.random.normal(size=size).reshape(-1, 2) + 3\n",
    "        return np.concatenate([x0, x1, x]), np.concatenate([np.zeros(size//2), np.ones(size//2), 2*np.ones(size//2)])\n",
    "    return np.concatenate([x0, x1]), np.concatenate([np.zeros(size//2), np.ones(size//2)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "model = MultiFisherLinearDiscriminant(n_classes=3)\n",
    "x_train, y_train = create_data(add_class=True)\n",
    "model.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train)\n",
    "x1_test, x2_test = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.concatenate([x1_test, x2_test]).reshape(2, -1).T\n",
    "y_pred = model.classify(x_test)\n",
    "x = np.linspace(-5, 5, 20)\n",
    "plt.contourf(x1_test, x2_test, y_pred.reshape(100, -1), alpha=0.2, levels=np.linspace(0, 1, 3), cmap=plt.get_cmap('YlOrBr'))\n",
    "# plt.scatter()\n",
    "plt.title('Fisher Discriminant')\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.7 ('torch10')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "vscode": {
   "interpreter": {
    "hash": "8f5c1b24a4ab56abd916d54534896e4f6d0a89a0daba3b8db7ea16393a780e2e"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}